Quiver Asymptotics: $\mathcal{N}=1$ Free Chiral Ring

Abstract

The large N generating functions for the counting of chiral operators in $\mathcal{N}=1$, four-dimensional quiver gauge theories have previously been obtained in terms of the weighted adjacency matrix of the quiver diagram. We introduce the methods of multi-variate asymptotic analysis to study this counting in the limit of large charges. We describe a Hagedorn phase transition associated with this asymptotics, which refines and generalizes known results on the 2-matrix harmonic oscillator. Explicit results are obtained for two infinite classes of quiver theories, namely the generalized clover quivers and affine ${\mathbb{C}}^3/{\hat{A}}_n$ orbifold quivers.

19 pages, 8 figures, some clarifications on minimal critical points are added